Consider the optimal control problem for the two processor flow-shop when processing times for n tasks are (linear) functions of the state. Since the latter also depends on the sequence, a hierarchical approach is proposed. We solve here, for any given sequence, the problem of optimally launching the tasks using the idle time of the first processor (P₁) at stage as the control parameter if i^th task. In particular, we show that makespan associated to a given sequence is minimized when P₁'s idle time is concentrated on some critical parts determined by the schedule. Also, our results suggest how to devise a fast heutistic algorithm, and propose interesting bounds for a branch-and-bound approach to the scheduling problem.